Find the form of all n in N satifying tow(n)=6. (sorry don't know how to write this Tex). What is the smallest positive integer n for which this is true?
tow(n)=6 so 6=(1+a1)(1+a2)----(1+ak) where n=p1^a1p2^a2---pk^ak
$\displaystyle \tau(n)=6$
We have $\displaystyle \tau(n)=(1+\alpha_{1})(1+\alpha_{2}).....(1+\alpha _{k})$for k=$\displaystyle p^{\alpha_{1}}p^{\alpha_{2}}...p^{\alpha_{k}}$
So $\displaystyle 6=(1+\alpha_{1})(1+\alpha_{2}).....(1+\alpha_{k})$
I just don't know about the next step...